// Copyright (c) 2021, gottingen group.
// All rights reserved.
// Created by liyinbin lijippy@163.com

#ifndef TEST_TESTING_CHI_SQUARE_H_
#define TEST_TESTING_CHI_SQUARE_H_

// The chi-square statistic.
//
// Useful for evaluating if `D` independent random variables are behaving as
// expected, or if two distributions are similar.  (`D` is the degrees of
// freedom).
//
// Each bucket should have an expected count of 10 or more for the chi square to
// be meaningful.

#include <cassert>
#include "abel/base/profile.h"

namespace abel {

namespace random_internal {

constexpr const char kChiSquared[] = "chi-squared";

// Returns the measured chi square value, using a single expected value.  This
// assumes that the values in [begin, end) are uniformly distributed.
template<typename Iterator>
double chi_square_with_expected(Iterator begin, Iterator end, double expected) {
    // Compute the sum and the number of buckets.
    assert(expected >= 10);  // require at least 10 samples per bucket.
    double chi_square = 0;
    for (auto it = begin; it != end; it++) {
        double d = static_cast<double>(*it) - expected;
        chi_square += d * d;
    }
    chi_square = chi_square / expected;
    return chi_square;
}

// Returns the measured chi square value, taking the actual value of each bucket
// from the first set of iterators, and the expected value of each bucket from
// the second set of iterators.
template<typename Iterator, typename Expected>
double chi_square(Iterator it, Iterator end, Expected eit, Expected eend) {
    double chi_square = 0;
    for (; it != end && eit != eend; ++it, ++eit) {
        if (*it > 0) {
            assert(*eit > 0);
        }
        double e = static_cast<double>(*eit);
        double d = static_cast<double>(*it - *eit);
        if (d != 0) {
            assert(e > 0);
            chi_square += (d * d) / e;
        }
    }
    assert(it == end && eit == eend);
    return chi_square;
}

// ======================================================================
// The following methods can be used for an arbitrary significance level.
//

// Calculates critical chi-square values to produce the given p-value using a
// bisection search for a value within epsilon, relying on the monotonicity of
// chi_square_p_value().
double chi_square_value(int dof, double p);

// Calculates the p-value (probability) of a given chi-square value.
double chi_square_p_value(double chi_square, int dof);

}  // namespace random_internal

}  // namespace abel

#endif  // TEST_TESTING_CHI_SQUARE_H_
